POST UTME IMS U 2020 Mathematics | Objective

Practice these randomly selected questions to test your readiness.

Question 1
Two events, A and B, are indep\endent. If P(A) = 0.4 and P(B) = 0.6, find P(A ∩ B).
A. 0.12
B. 0.24
C. 0.36
D. 0.48
Question 2
Solve the system of equations \( x + y = 4 \) and \( xy = 5 \).
A. \( x = 1, y = 3 \)
B. \( x = 2, y = 2 \)
C. \( x = 3, y = 1 \)
D. \( x = 4, y = 0 \)
Question 3
Find the determinant of the matrix [ egin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \ 7 & 8 & 9 \end{pmatrix} ].
A. 0
B. 1
C. 2
D. 3
Question 4
A sequence is defined by \( a_n = 2n + 1 \). Find the sum of the first 5 terms of the sequence.
A. ( 15 )
B. ( 20 )
C. ( 25 )
D. ( 30 )
Question 5
Solve the quadratic equation \( x^2 + 5x + 6 = 0 \) u\sing the quadratic formula.
A. \begin{pmatrix} -2 \ 3 \end{pmatrix}
B. \begin{pmatrix} -3 \ 2 \end{pmatrix}
C. \begin{pmatrix} 2 \ -3 \end{pmatrix}
D. \begin{pmatrix} 3 \ -2 \end{pmatrix}
Question 6
A particle moves in a straight line with its position given by $s(t) = 2t^3 - 5t^2 + 3t + 1$. Find the velocity of the particle at $t = 2$ seconds.
A. -14
B. -10
C. 10
D. 14
Question 7
Solve for ( x ) in the equation \( egin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} egin{bmatrix} x \ 1 \end{bmatrix} = egin{bmatrix} 7 \ 10 \end{bmatrix} \).
A. 2
B. 3
C. 4
D. 5
Question 8
Find the equation of the circle with center \( -2, 3 \) and radius 4.
A. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )
Question 9
A box contains 5 red balls and 3 blue balls. If a ball is drawn at random, what is the probability that it is blue?
A. 1/2
B. 2/5
C. 3/8
D. 1/3
Question 10
Find the surface area of the sphere with radius $r = 4$ cm.
A. 32π
B. 64π
C. 128π
D. 256π
Question 11
Find the value of [ \log_{10} \( x^2 \) = 4 ].
A. 10
B. 100
C. 1000
D. 10000
Question 12
Find the mean of the data set: 2, 4, 6, 8, 10. If the mean is increased by 2, what is the new mean?
A. 12
B. 14
C. 16
D. 18
Question 13
A set ( S ) is defined as \( S = { x | x in mathbb{R}, x > 0 } \). Find the complement of ( S ).
A. \( { x | x in mathbb{R}, x leq 0 } \)
B. \( { x | x in mathbb{R}, x geq 0 } \)
C. \( { x | x in mathbb{R}, x < 0 } \)
D. \( { x | x in mathbb{R}, x > 1 } \)
Question 14
A rec\tangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. Find its volume.
A. 30
B. 50
C. 60
D. 70
Question 15
Find the equation of the circle with center \( -2, 3 \ \) ) and radius 4.
A. \( x + 2 \ \)^2 + \( y - 3 \)^2 = 16 )
B. \( x - 2 \ \)^2 + \( y + 3 \)^2 = 16 )
C. \( x + 2 \ \)^2 + \( y + 3 \)^2 = 16 )
D. \( x - 2 \ \)^2 + \( y - 3 \)^2 = 16 )

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